(3 0 £

NBS

Reference

PUBL| CATI0NS

NBSIR 84-3015

mum A 111 Ob H2flfl34

A PRELIMINARY INVESTIGATION INTO

USING THE SUN AS A SOURCE FOR G/T

MEASUREMENTS

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303

August 1984

-QC

100

. U56

84-3015

1984

JJATIOHAI. BUREAU Of STANDARDS

LIBRARY

NBSIR 84-3015

A PRELIMINARY INVESTIGATION INTO

USING THE SUN AS A SOURCE FOR G/T

MEASUREMENTS

William C. Daywitt

Electromagnetic Fields Division

National Engineering Laboratory

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303

August 1984

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

CONTENTS

Page

1. Background and Introduction 1 2. Determination of the Solar Flux Density Above 5 GHz

2.1 Strategy

2.2 Flux Density

2.3 Errors

3. Star Shape Correction Factor

4. Discussion and Conclusions

5. Acknowledgments

6. References

i i i

A Preliminary Investigation Into Using the Sun

as a Source for G/T Measurements

Wi 1 1 i am C . Daywitt

Electromagnetic Fields Division

National Bureau of Standards

Boulder, Colorado 80303

This report describes a preliminary investigation into determining the solar

flux density, the atmospheric correction factor, and the star shape correction

factor for use in G/T measurements above 5 GHz. An estimate of errors is also

included. Preliminary results show: an improved algorithm for determining

diffusive and refractive attenuation; a viable technique for estimating the solar

flux density from daily AFGL flux density measurements and a centimeter/millimeter

wave spectrum function; and the possibility of reducing star shape correction factor

errors by use of an effective solar rf diameter.

Key words: atmospheric correction factor; earth terminal measurement system; error

analysis-, G/T; solar flux density; star shape correction factor.

1. Background and Introduction

The Electromagnetic Fields Division of the National Bureau of Standards has successfully made

precision G/T (gain to system noise temperature) measurements [1] on low noise, large diameter

(11 m to 28 m) antenna systems using the radio star Cassiopeia A, and on medium size (4 m to 6 m)

antenna systems using the moon. Although the moon is an attractive source to use with these

smaller systems because of its predictable radio output [2], in many cases [3] the system noise is

so much greater than the received lunar output that the measurement sensitivity is too low to be

useful. Since the solar angular diameter is about that of the moon and its output is considerably

greater, the sun provides an answer to the sensitivity problem. Unfortunately, its flux density

and brightness distribution are variable, and even with this preliminary study a number of

investigations are still needed to determine the correct G/T measurement error. This report

describes an effort to determine the feasibility of using the daily Air Force Geophysics

Laboratory (AFGL) flux density values [4] measured at the Air Force Sagamore Hill Observatory in

Hamilton, Massachusetts. The results pertain to frequencies above 5 GHz for reasons that will be

made clear later.

The antenna system G/T can be expressed as

G _8-nk ( Y - 1) T 2 x Sk

1 k 2

where k is Boltzmann's constant, Y is the ratio of the power measured with the sun in t h e

- a mainbeam to the power measured with the antenna pointed at the cold sky, \ is the v. • •• •

wavelength, S is the solar flux density incident on the earth's atmosphere, and k| a" 1

• , atmospheric transmission and star shape correction factors respectively [5].

1
The atmospheric transmission factor accounts for the reduction in the received flux and is

due to three atmospheric phenomena [6], gaseous attenuation, refractive spreading of the incident

wavefront, and incoherent tropospheric scattering. It does not include attenuation and scattering

from clouds, rain, fog, hail, or snow since the precision measurements envisioned here are assumed

to be performed in clear, stable weather. If A is the total zenith attenuation in decibels due to these three phenomena, then

kj . i 0

-'vl0s1,w

(2)

where 0 is the elevation angle to the source relative to the antenna location on the earth's

surface. Details of a simplified calculation for the gaseous component of A are described

elsewhere [7],

An algorithm derived in an earlier analysis [5] for the zenith attenuation due to the

tropospheric scatter of the energy from a point source radio star and intended for the 1 GHz to 10 GHz frequency range diverges above 10 GHz. Since that analysis, further measurement data [8] has come to light which provides a more detailed picture of this attenuation. The resulting curves derived from the data and which include the refractive attenuation are shown in figure 1. The

first set of data [6] were taken at 4.17 GHz and 6.39 GHz with a 22 m antenna, and the second set

[8] at 15.5 GHz and 31.6 GHz with a 7 m antenna. The dashed curves through the two sets of data

points are parallel, and suggest a family of straight lines for other antenna diameters. A linear

interpolation in antenna diameter between the two dashed curves produced the linear portions of the curves shown. Since theory [6] indicates that the attenuation decreases with decreasing

frequency, the curves were extended accordingly. When the angular diameter of the source is finite, the attenuation is reduced [6], decreasing as the ratio of source diameter to antenna

beamwidth increases. The equation in figure 1 descibes this effect [5] where d is the source

diameter, is the half-power beamwidth, A

Q

is the zenith attenuation for a point source given by

the curves in the figure, and A is the corresponding attenuation for the finite source diameter.

An earlier investigation [5] indicates that the total error in these attenuation curves and the

non-point source correction is probably in the neighborhood of 50%.

The star shape correction factor accounts for variation of the solar brightness distribution

across the antenna beam pattern, and vanishes as the ratio of the angular source diameter to the

antenna half-power beamwidth vanishes. In terms of a distribution B and a normalized power

pattern P

n

,

/ B(q)P (r) do

k 2 = / B(r) dR (3)

where R represents the two antenna pointing angles and dR is the differential solid angle. The

integral in the denominator is equivalent to the flux density S.

Sections 2 and 3 present the results of a preliminary investigation into the determination of

the flux density S and the star shape correction factor

2
2. Determination of the Solar Flux Density Above 5 GHz

2.1 Strategy

Solar radio emission is the result of three superimposed sources of radiation [9], the quiet,

slow, and burst components. The quiet sun emission comes from unlocalized, thermal sources in the

solar atmosphere (chromosphere and corona), and is constant over periods of months to years. The

slow component also has a thermal origin and originates in local sources in the vicinity of

sunspots and chromospheric plagues. These partially polarized sources have periods of days,

weeks, or months. The burst components are the results of thermal, synchrotron, and plasma

radiation from transient sources such as flares, and are partially polarized. Their recurrence

frequency and period are small for the quiescent portion of the solar cycle, increasing to two or more per a 10-hour viewing day during the active portion, which suggests the possibility of making

G/T measurements using the sun without encountering a burst during the process. The fact that the

quiet and slow components have periods of greater than a day further suggests the possibility of

using an average of two successive daily AFGL flux density values to determine the flux at the

time of the G/T measurement taking place between the two AFGL measurements.

Figure 2 depicts the average solar flux density spectrum incident on the earth's atmosphere

[10] with an insert [11] indicating the duration of the burst spectrum from 10 MHz to 30 GHz. The

quiet component of the solar emission dominates above 5 GHz, at which frequency most of the burst

components have disappeared and the slow component is falling off. The insert shows that the

duration of the remaining burst continuum is short. Thus, the solar emission above 5 GHz is

relatively stable from day to day as long as the type IV bursts are avoided, again suggesting a G/T measurement scheme using AFGL flux density values.

Superimposed on the graph of figure 2 are three sets of hashmarks representing monthly

averages of AFGL flux density measurements (with atmospheric attenuation removed) [4] from January

1979 to May 1982. The measurement values approach the average quiet sun value between the

"sunspot (s.s) max" and the "s.s. min" curves as the frequency increases. Thus, above the highest

AFGL measurement frequency (15.4 GHz), apparently the average of the quiet sun curves can be used

to determine the flux density incident on the earth's atmosphere. Following is an approximate

equation giving this average that was derived by least-square fitting the average data

corresponding to the quiet sun curves in the figure and in table 1 (from reference [10]):

The flux density S and the frequency f are the same units as the figure. The following equations

can be used to extrapolate between the AFGL measurement frequencies [12]:

log S = 1.20 + 1.10 (log f) + 0.179 (log f) 2

. ( 4 )

where

1 n Cf /f !

)

( 6 )

S has the same units (W/M

2 /Hz) as the graph, and f i and f£ correspond to Sj

3

and S^.
respectively. The subscripts denote the two AFGL values of flux density and frequency between

which the flux density S at frequency f is desired.

The preceding discussion suggests the following strategy for determining the solar flux

density above 5 GHz: 1) if the G/T measurement frequency is 4.995 GHz, 8.8 GHz, or 15.4 GHz, use

an average of two adjacent daily AFGL flux values; 2) if the measurement frequency is between two AFGL frequencies, use the average determined in 1) for both AFGL frequencies and translate the

result to the desired frequency via eqs (5) and (6); and 3) if the frequency is above 15.4 GHz, use eq (4) to determine the flux density. Since the reported AFGL flux density values are corrected for bursts, it is only then necessary to insure that the G/T measurement did not take

place duri ng a burst

.

To illustrate, suppose a series 10 GHz G/T measurements were performed in Boulder, Colorado,

at various times between 7 a.m. (1400 u.t. (universal time)) and 5 p.m. (2400 u.t. local standard

time on October 17 , 18, 19, 1983. The appropriate AFGL flux density values (in units of 10“^

W/m/Hz) that bracket 10 GHz on these days are isolated in the box of figure 3 for the month in

question [4]. The "C" value from eq (6) for the frequencies indicated (8.8 GHz, 10 GHz, 15.4 GHz)

turns out to be 0.7716 (with f^ = 8.8, f = 10, and ^

~ 15.4). Using this value, the flux

densities in the box, and eq (5), the 10 GHz flux density values at the AFGL measurement time

(approximately 1630 u.t.) on the 17th, 18th, 19th, and the 20th are 334, 321, 330, and 326,

respectively. Linear interpolation between any appropriate two of these values will then yield

the correct flux value for a specific Boulder G/T measurement time. Figure 4 is a reproduction of

another page from the "Solar-Geophysical Data" report that indicates the time and size (in flux

density unito) of any bursts that have taken place during the days in which the G/T measurements

were being performed. The data in the boxes show the larger microwave bursts taking place during

the G/T measurement times in question (1400 u.t. to 2400 u.t.), and thus any G/T measurements

performed during these bursts c hould be discarded. The smaller bursts shown in the figure,

although somewhat arbitrarily excluded, have a less significant effect on the G/T measurement.

2.2 Flux Density

For simp'Mcity the preceding illustration ignores atmospheric attenuation and the true earthsun distance at the time of thp G/T measurements. A complete flux density determination between

AFGL frequencies proceeds as follows: 1) calculate the flux densities S-^ and S

2 corresponding to

the appropriate two AFGL frequencies for the G/T measurement time between the two AFGL daily

measurements; 2) adjust and S

2 for the true earth-sun distance (the values reported in figure 3 are normalized to 1 astronomical unit); 3) remove the effects of atmospheric attenua'^on from

and S

2 via eq (2); 4) use eqs (5) and (6) to obtain the flux density S incident on tlr " ch's

atmosphere at the G/T measurement frequency; and 5) apply eq (2) a second time at the measurement

frequency to obtain the flux density at the location on the earth's surface where the G/T

measurement is performed. Above 15.4 GHz eq (4) can be used to estimate the flux density incident

on the atmosphere, after which step 5 is applied.

Prior to, but not afterward, January 1980, AFGL removed the effects of atmospheric attenuation from their measurements and reported flux density values incident on the atmosphere.

Therefore, the flux density values reported in figure 3 contain the atmospheric attenuation.

4
To illustrate, suppose a G/T measurement is performed at an antenna site in Boulder on October 17, 1983, as the sun transits the local meridian (1848 u.t. [13]). The AFGL flux density

values measured earlier on the 17th and on the following day during meridian transit (1630 u.t.

[13]) at the Sagamore Hill Observatory are reported (fig. 3) as 282 and 268 at 8.8 GHz, and as 588

and 587 at 15.4 GHz. By a linear extrapolation in time between these daily measurements, flux

density values at 1848 u.t. of 280.6 and 587.9 are obtained for 8.8 GHz and 15.4 GHz,

respectively. The true earth-sun distance (in units of 1 astronomical unit) at 1848 u.t. on the

17th was 0.996 [13]. Thus, the true flux density values at the G/T measurement time are a factor

of 1 .008 (0.996

- ^) larger than the values reported by AFGL, or 282.8 and 592 .6 for 8.8 GHz and

15.4

GHz, respectively.

The average solar declination during the AFGL and G/T measurements was a negative 9.4 degrees

[13]. Combined with the Sagamore Hill latitude of 40.6° north, this leads to a solar elevation

angle at that site of 38.0°. The zenith values for the gaseous component of the atmospheric

attenuation in October at the observatory are [7] 0.042 dB and 0.080 dB for 8.8 GHz and 15.4 GHz,

respectively. The zenith values for the diffusive and refractive attenuation for the average

solar diameter of 0.58° [13] during the measurements are (fig. 1) 0.012 dB at 8.8 GHz and 0.015 dB

at 15.4 GHz. Combining these with the gaseous components gives a total zenith attenuation of

0.054 dB at 8.8 GHz and 0.095 dB at 15.4 GHz. These latter values with the 38.0° declination lead

via eq (2) to atmospheric correction factors of 0.980 at 8.8 GHz and 0.965 at 15.4 GHz. Dividing

the previous flux density values by these correction factors leads to 288.6 and 614.1 at 8.8 GHz

and 15.4 GHz, respectively, for the flux densities incident on the atmosphere. Equations (5) and

(6) can now be used to obtain an estimate of the 10 GHz flux density and results in a value

342.9. If the Boulder site is at 40° north latitude, the solar elevation angle there is 40.6°.

Combining a gaseous attenuation of 0.029 dB [7] with a diffusive and refractive attenuation of

0.011 dB (fig. 1) yields a correction factor of 0.986 for a 40.6° elevation angle, resulting in a value of 338.1 for the flux density at the Boulder site.

2.3 Errors

The total error in determining the flux density from the AFGL measurements is the sum of four

parts: the AFGL measurement error; the error in using eqs (5) and (6) to extrapolate between AFGL

frequencies; the error in estimating the atmospheric transmission factor; and the error in

estimating the flux density by the linear time interpolation between the daily AFGL

measurements. This latter error for frequencies above the highest AFGL frequency (15.4 GHz) is at present taken as the maximum error (halfway) between the highest AFGL frequencies, 8.8 GHz and

15.4

GHz.

The AFGL error for measuring the flux density is 5% [12].

An error of 1% is assigned to the uncertainty in extrapolating between AFGL frequencies, and

was determined by comparing the 8.8 GHz average value (average of the AFGL hashmarks in figure 2)

with the 8.8 GHz value obtained via eqs (5) and (6) and the average AFGL values at 4.995 GHz anc

15.4

GHz.

The total (gaseous + diffusive + refractive) zenith attenuations for Boulder at 10 GHz r : Sagamore Hill at 8.8 GHz and 15.4 GHz are 0.040 dB, 0.054 dB, and 0.095 dB, respectively,

these values are uncertain by 50% [5], leading to transmission coefficient errors of 0.7 ,

.

5
and 1.8%, respectively. The overall transmission coefficient error is a weighted sum

(0 .7+cxl .0+( 1-c )xl .8) of these separate errors with a value of approximately 2% for the value of C determined in section 2.1.

Figure 5 is a plot of a number of hypothetical smoothed flux density curves between the AF6L

values of S(t^) and S(t 2

) measured during meridian passage at time tj and time t

2 the following

day (t^ - t^ + 24 hours). The linear curve whose equation is shown in the figure was previously

used to estimate the flux density at time t between the AFGL measurement times t^ and t

2

, where h

is the relative forward interval between t^ and t. S(t) is the flux density at t for the true

(but unknown) curve, and a

s is the estimated standard deviation of the possible values at t for

the probability density curve shown. The forward relative interval h is defined in the figure.

AS is defined to be the difference between the linear approximation and the unknown flux density

S(t), and is therefore a random variable whose estimated standard deviation a is a measure of the

A error in using the linear approximation. A simple analysis of the situation depicted in the

figure shows that the two standard deviations are related by the equation

where p, is the estimated autocorrelation function [14] between measured flux density values 24

L h 1 h hours (= t^ - t^) apart. and p^

- are, respectively, approximations to the autocorrelation

functions between flux density values t - tj and t

2

- t apart. The flux-density variations are assumed to be sufficiently stationary for eq (7) to give some indication of the time interpolation

error

.

Figure 6 shows a plot of the 8.8 GHz AFGL flux density values measured from January through

June 1979. The change of levels at LI, L2, and L3, and the slopes at SI, S2, and S3 indicate that

the variation is not stationary and should possibly be modeled [14] as an ARIMA (p ,1 ,q ) or an ARIMA (p,2,q) process to estimate the standard deviation of the residual day-to-day fluctuations

of interest. However, for a preliminary (and more conservative) estimate of o

s

, the data shown

was assumed to be stationary, resulting in a value of 24 for o

s and a value of 0.9 for p-^. With

these values eq (7) is approximated by

This equation shows a maximum of 5.5 halfway between tj and t

2

, and is assumed to hold for the

entire range from 5 GHz to 15.4 GHz. For the illustration in section 2.2, h has the value of

0.096 (( 18 .8-16 .5 ) / 24 ) , yielding an estimated standard deviation from eq (8) of 3.2 or 1% (3.2/337), or a 3a error of approximately 3%.

Collecting the previous errors leads to a total error of 11% (3a) in determining the solar

flux density for the illustration presented in section 2.2. The error at lower elevation angles

and/or higher frequencies will be greater, primarily because of increased gaseous attenuation.

3. Star Shape Correction Factor

For antenna half-power beamwidths (HPBW) greater than about five angular source diameters,

examination of eq (9) shows that ratio in eq (3) can be replaced by unity with an error less than

- 2a^[l - h + h^ + h(l-h) p

^ - (l-h)p^ - hpj ^] (7)

( 8 )

6
l‘t. . To use the cel estial -source method of measuring G/T accurately below five source diameters,

however, an estimate of the variation of the source brightness distribution across the antenna

mainbeam indicated in the numerator of eq (3) must be made. For sources with stable and

predictable distributions and Gaussian mainbeams, this can be accomplished by replacing the ratio

in eq (3) by a simple formula depending only upon the ratio of HPBW to source diameter.

Furthermore, if the source diameter is properly chosen, the formula will provide an accurate

estimate of the correction factor for any HPBW/di ameter ratio above unity [15,2]. As will be seen there is reason to expect that this technique will also work for the sun, even though the solar

brightness distribution is continuously changing. Errors in the star shape correction factor have

not yet been investigated.

For a source resembling a circular disk and a Gaussian mainbeam, eq (3) leads to

where

2

x

2

1 n2 .

( 9 )

( 10 )

d is the effective rf angular diameter of the source, and is the antenna HPBW. The diameter is

chosen to minimize the difference

1 - e“

x

/ B (q

)

P

n (Q) dQ

x

2

/ B(q) dQ

(ID

for e H/d greater than unity. The same expressions (eqs (9) and (10)) hold for an elliptical disk

O with d

c replaced by the product of the major and minor source diameters. No significant reduction

in the difference in eq (10) is achieved with this latter model, however, even though the solar

brightness distribution shows a decided ellipticity (fig. 7, [9]).

Figure 2 shows that, except for the burst components which are assumed to be missing during

the G/T measurement, the quiet sun emission plays an increasingly dominant role in the total

emission above 5 GHz where the slow component begins to fall off. Furthermore, observations of

the solar brightness distribution in the decimeter, centimeter, and millimeter wave frequency

regions reveal that, although the effective brightness temperature varies with the solar cycle,

the distributions remain relatively constant [9]. It is this constant part of the brightness

distribution that will presumably be amenable to the technique of the previous paragraph, wit’! fluctuations in the result coming from the more variable slow emission component. The degree of success will depend upon how minor these fluctuations turn out to be, but hopefully at least siraccuracy in k£ will be gained below five source diameters. This question can only be de-rv:

after a number of distributions at various frequencies and at various times during the solar cy< 1- have been convoluted with the antenna beam pattern. To date this has not been done.

Since the effective diameter or diameters for the solar distributions have not yet

determined, the question of what diameter d to use in eq (10) remains. A glance at f 1

, r - •

7
that the polar profiles tend to average out as a constant up to the optical diameter, with the

equatorial profile averages extending somewhat beyond. This situation implies that the effective

rf diameter will extend beyond the optical diameter, which in turn will depend upon the results

from convolving the brightness distributions with the Gaussian beam pattern. Based on a circular

disk model of the quiet-sun atmosphere with a constant chromospheric temperature of 3 x 10^

kelvins and a coronal temperature of 10® kelvins, Smerd [16] calculated a brightness temperature

distribution and compared it to the apparent brightness temperature derived from the same model.

The apparent temperature is defined as the temperature of a blackbody having the same diameter as the optical disk and radiating the same apparent flux density. The results are shown in figure 8 where the ratio of two particular brightness temperature contours to the apparent temperature are plotted. The upper curve is where the contour temperature falls to IX of the apparent temperature

and the lower curve is where it falls to 10%. As expected the ratios approach unity with

increasing frequency as the origin of the radiation is increasingly confined to the

chromosphere. The dashed line approximating the 10% curve and ending at 30.3 GHz will be used

temporarily to define the effective diameter for eq (10). Thus,

d = d o

1 .240-0.162 log f, 5<f<30.3

1 , f> 30.3

( 12 )

where d

Q is the optical diameter obtained from the Astronomical Almanac [13] at the time of the

G/T measurement. For the illustration in section 2.2, the Boulder antenna diameter is 4.3 m (fig.

1) yielding a 10 GHz HPBW of 0.49°. At the measurement time the optical solar diameter was 0.54°

[13] which yields an rf diameter via eq (12) of 0.58°. Equations (9) and (10) then give a star

shape correction factor of 0.64.

4. Discussion and Conclusions

The curves in figure 1 used for determining the diffusive and refractive attenuation fc-' a point source, although quite rough and incomplete, offer an improvement over the previous

algorithm [5] that diverges above 10 GHz.

The total error in estimating the solar flux density from 5 GHz to 15.4 GHz in clear, stable,

weather is 11%, and is the sum of 5% for the AFGL measurements, 1% for extrapolati ng between two

AFGL frequencies, 3% for estimating the flux density between the daily AFGL measurement times,

1.3% for removing the atmospheric attenuation from the AFLG measurements, and 0.7% for estimating

the atmospheric attenuation at the G/T measurement frequency. Discarding the 0.7% error, the sum

comes to about 8%, and represents the error in determining the flux density incident on the

earth's atmosphere. Since the average of the AFGL hashmarks in figure 2 approaches the area between the "s .s . max" and "s.s. min" curves as the frequency increases, and since their spread

and that between the curves decreases with frequency, it appears that an 8% error in using eq (4) to determine the solar spectrum above 15.4 GHz incident on the earth's atmosphere is reasonable

for the spectrum shown in the figure.

The brightness distribution of the quiet sun above 5 GHz is relatively insensitive to the

solar cycle. This, coupled with the fact that the quiet-sun component also dominates above this

frequency, implies the possibility of finding an effective rf diameter (as a function of frequency) that minimizes the error in using the circular disk approximation to the star shape

8
correction factor in eq (3), improving G/T measurement accuracy for HPBW/source-di ameter ratios

between one and five.

Although the preceding conclusions appear to be reasonable, there still remains a considerable amount of work to be completed before final acceptance.

The majority of the work described in this report was carried out in 1979 and was part of a larger effort to design and construct an earth terminal measurement system capable of precision

antenna system measurements. Therefore, much of the direction and inspiration for this work came from other individuals associated with the project, principally David Wait and John Wakefield.

6. References

[1] Wait, D. F. Precision measurements of antenna system noise using radio stars. IEEE Trans,

on I&M, Vol. IM-32, No. 1: 110-116; 1983 March.

[2] Daywitt, W. C. An error analysis for the use of presently available lunar radio flux data

in broadbeam antenna-system measurements. Nat. Bur. Stand. (U.S.) Tech. Note 1073; 1984

February

.

[3] Wait, D. F.; Daywitt, W. C. Preliminary examination of 20 GHz G/T measurements of earth

terminals. Nat. Bur. Stand. (U.S.) Int. Rpt. 83-1686; 1983 March.

[4] Solar-Geophysical Data; prompt reports. Ed. H. E. Coffey; No. 470, Part 1, 1983 November.

[5] Daywitt, W. C. Error equations used in the NBS precision G/T measurement system. Nat. Bur. Stand. (U.S.) Int. Rpt. 76-842, 1976 September.

[6] Yokoi, H.; Yamada, M.; Satoh, T. Atmospheric attenuation and scintillation of microwaves

from outer space. Publ . Astr. Soc. Japan, Vol. 22, No. 4, 511-524; 1970.

[7] Daywitt, W. C. Atmospheric propagation equations used in the NBS earth terminal

measurement system. Nat. Bur. Stand. Int. Rpt. 78-883, 1978 April.

[8] Yokoi, H.; Yamada, M. Measurements of earth-space propagation characteristics at 15.5

and 31.6 GHz using celestial radio sources. Trans. IECE '74/2, Vol. 57-B, No. 2; 121-1. . 1974 February.

[9] Kundu, M. R. Solar Radio Astronomy. New York, N.Y.: Interscience Publishers; 1965.

[10] Allen, C. W. Astrophysi cal Quantities. London: The Athlone Press/University of . 1976.

9
[11] Mangis, S. J. Introduction to sol ar-terrestri al phenomena and the space environment

services center. NOAA Tech. Rpt. ERL 315-SEL 32, 1975 January.

[12] Guidice, D. A.; Castelli, J. P. The use of extraterrestrial radio sources in the

measurement of antenna parameters. IEEE Trans. Aerospace and Electronic Systems: Vol . AES-7, No. 2; 226-234; 1971 March.

[13] The Astronomical Almanac for the Year 1983. Washington: U.S. Government Printing Office.

[14] Box, G. E. P.; Jenkins, G. M. Time Series Analysis —Forecasting and Control. San Francisco: Holden-Day; 1976.

[15] Kanda, M. An error analysis for absolute flux density measurements of Cassiopeia A. IEEE Trans, on I&M, Vol. IM-25, No. 3; 173-182; 1976 September.

[16] Smerd, S. F. Radio-frequency radiation from the quiet Sun. Aus. J. Sci . Res., A3 , 34; 34-

59; 1950.

10
0.07

o

CD in ro CM

O o o O o

d o o o o

(SP) °V N0llVnN311V H1IN3Z

>-

O

LlI 3

O

LlI

ir

Li11

Figure

1.

Diffusive

and

refractive

attenuation

A

Q

for

a

point

source.

The

equation

appearing

in

the

upper

left

corner

of

the

figure

is

used

to

estimate

the

attenuation

A

for

a

non-point

source

(d*

0)

once

A

n

has

been

determined

from

the

curves.
Solar

Flux

(W/m

2

/Hz)

Figure 2. Solar radio

reference [10].)

spectrum. (The symbols are explained more fully in

12
DAILY SOLAR INDICES

9 Oct 83

OCTOBER 1933

Julian

Bartel

s

Cyc le Sunspot

Numbers

Obs Flux Ottawa SGMR Solar

SGMR Flux AdjustedSGMR Ottawa

to 1 Astronomical Unit

SGMR SGMR SGMR SGMR SGMR Day Day Day R

i ra

. (2800) (15400) (8800) (4995) (2800) (2695) (1415) (606) (410) (245)

01 275 11 32 33 117.3 565 266 148 117.5 105 97 79 37 22 02 276 12 51 57 120.3 566 266 152 120.4 106 97 75 34 19 03 277 13 63 69 123.0 — — — 123.1 — — — — —

04 278 14 74 73 125.1 585 271 156 125.1 110 99 76 33 15 05 279 15 65 59 126.6* 586 286 160 126.6* 121 103 80 33 23

06 280 16 75 76 132.8 592 277 161 132.7 127 106 82 34 17 07 281 17 87 86 134.0 596 281 158 133.9 103 109 87 36 , 19 08 282 18 99 89 131.4* 582 280 157 131.1* 113 1 1

87 36 22 09 283 19 106 100 130.8 580 276 156 130.4 109 112 85 39 36 10 284 20 108 113 134.0* 601 277 160 133.6* 1 15 1 19 84 35 24

1 1 285 21 130 134 138.9 593 271 164 138.3 121 118 83 37 19

1 2 286 22 122 114 134.2 570 265 157 133.7 1 10 113 73 32 16

1 3 287 23 100 94 134.2* 554 296 173 133.5* 121 1 14 87 37 15

i 4 288 24 75 73 132.2* 618 299 175 131.5* 1 19 110 82 2,5 16

1 5 289 25 72 64 127.8 — — — 127.0 — — -- "

16 290 26 61 55 1 18. 0A 605 284 161 1 17.2A 101 99 75 32 16

1 7 291 27 60 53 111.7* 588 282 152 110.9* 97 95 76 35 20 18 292 1 63 57 104.4 587 268 138 103.6 89 86 68 31 17 19 293 2 46 36 106.0 591 278 142 105.2 93 89 73 33 15 20 294 3 26 24 100.0 539 274 132 99.1 83 87 72 31 15

21 295 4 18 18 90.1 589 265 125 89.3 79 84 69 30 15 22 296 5 22 25 88.1 580 256 121 87.2 79 77 71 30 13 23 297 6 22 16 88.7 565 257 123 87.8 75 79 70 31 18 24 298 7 20 19 89.6 536 246 121 88.6 73 79 72 30 14 25 299 8 18 17 90.3 566 254 122 89.2 81 84 70 28 13

26 300 9 22 13 90.2 579 262 126 89.1 80 79 73 30 14 27 301 10 12 13 90.1 575 265 126 88.9 83 80 — 31 14 28 302 11 1

12 91 .6 578 256 124 90.4 84 79 74 34 15 29 303 12 16 0 92.0 571 259 124 90.7 78 76 68 29 14 30 304 13 15 8 93.9 565 252 124 92.6 82 80 50 26 14

31 305 14 19 15 97.0* 585 262 128 95.5* 86 83 73 28 15

Mean 55 52 112.4 581 270 143 111.7 97 95 76 32 17

Adjusted for burst in progress at time of measurement.

The observed and the adjusted Ottawa fluxes tabulated above are the "Series C" dally values reported by the Algonquin Radio Observatory, Ottawa, Ontario, Canada. The letter "A" following an enfry designates

an Interpolated flux. Numbers in parentheses In the column headings denote frequencies In MHz.

Equipment problems produced the gaps shown here In the Air Weather Service's Sagamore Hill (SGMR) obse>

vat i ons

.

The International and American sunspot numbers shown above are preliminary values.

Figure 3. Smoothed solar flux density (in units of W/m^/Hz) measured

the AFGL Sagamore Hill observatory (SGMR) at approximately solar

passage each day and adjusted to one astronomical unit. The box

the flux densities of interest.

daily by

meridian

contains

13
SOLAR RADIO EMISSION

SELECTED FIXED FREQUENCY EVENTS

29 Oct 83

OCTOBER 1983

Time of F 1 ux Density Start Max i mum Durat ion Peak Mean Day Freq Sta Type (UT) (UT) (Min) (10 -22 W/m 2 Hz) Int Remarks

1 7 r 8800 LEAR 8 s 0552.1 0552.8 1 .7 24.0 a=6 ST=2 TYP=3 L 2695 LEAR 8 s 0552.3 0552.8 .8 10.0 CL =6 ST=2 TYP=3

r-8800 LEAR 8 s 0940.1 0940.1 .4 30.0 QL=6 ST=2 TYP=3

L-2695 LEAR 8 s 0940.1 0940.1 .5 20.0 CL =6 ST=2 TYP=3 3200 BERN 4 S/F 1 140.5U 1141 .OU 4.0D 155. OU ONLY PAPER REC

r-8800 ATHN 4 S/F 1207.3 1213.5 12.8 21 .0 CL =6 ST=2 TYP=3

L-3800 SGMR 8 S 1213.1 1214.6 1 .5 20.0 Cl =6 ST=3 TYP=3 2800 0TTA 21 GRF 1520.0 190.0 2.4 2800 0TTA 1 s 1634.0 1634.2 5.0 6.0 1 .2 2800 0TTA 1 s 1658.0 1658.4 2.0 1 .8 2800 0TTA 1 s 1718.9 1719.0 1 .0 1 .8 .8 2800 0TTA 8 s 2029.0 2029.3 .5 7.0

1 8 8800 LEAR 20 GRF 0143.5 0144.8 7.5 9.0 CL =6 ST=2 TYP=2 8800 LEAR 8 s 0346.3 0347.0 2.0 10.0 QL=6 ST=2 TYP=3 8800 LEAR 4 S/F 0350.3 0351 .0 8.7 9.0 CL =6 ST=2 TYP=3

r 8800 SGMR 47 GB 1924.6 1925.6 3.7 139.0 CL =6 ST=2 TYP=5

L 8800 PALE 47 GB 1924.8 1925.6 2.0 1 19.0 CL=6 ST=2 TYP=5 -2800 OTTA 3 S 2105.0 2106.5 5.0 10.4 4.0 -2695 PALE 8 s 2106.0 2106.8 1.1 17.0 CL =6 ST=2 TYP=3

-|8800 PALE 8 s 2106.3 2106.3 .5 27.0 CL =6 ST=2 TYP=3

19 2800 OTTA 240 R 1426.0 1431 .0 5.0 2.4 1 .6 2800 OTTA 1 s 1444.0 1447.0 7.0 8.0 3.0 2800 OTTA 21 GRF 1444.0 1450.0 40.0 2.4 1.2 -2695 SGMR 8 S 1446.1 1446.6 1 .2 16.0 CL =6 ST=2 TYP=3

-13800 SGMR 8 s 1446.5 1446.6 .6 16.0 CL =6 ST=2 TYP=3 2800 OTTA 21 GRF 1 750.0 1905.0 320.0 6.4 2300 OTTA 28 PRE 1959.0 2000.

0

4.0 3.8 1 .9 8800 SGMR 47 GB 1959.1 2009.3 15.4 200.0 CL =4 ST=2 TYP=5 9800 PALE 8 S 1959.6 1959.8 1.0 45.0 QL=6 ST=2 TYP=3

- 2695 PENT 4 S/F 2003.0 2009.2 15.0 265.0 34.0

-J 8800 PALE 47 GB 2004.0 2006.1 15.6 160.0 CL =6 ST=2 TYP=5 -2695 PALE 47 GB 2005.8 2006.

1 1 .0 21 .0 CL =6 ST=2 TYP=5 -2695 SGMR 47 GB 2005.8 2009.3 9.7 150.0 QL = 4 ST=2 TYP=5 2800 OTTA 29 PBI 2018.0 2018.0 130.0 1 1 .8 4.9

24 2695 PALE 8 S 1840.1 1840.3 .4 29.0 CL =6 ST=2 TYP=3

29 2800 OTTA 2 S/F 1925.5 1930.8 7.5 6.8 2.6 2800 OTTA 29 PBI 1933.0 1933.0 10.0 1 .8 .9

31 2800 OTTA 23 GRF 1610.0 1820.0 300.00 12.8

- 2800 OTTA 4 S/F 161 3.0 1616.1 6.0 30.0 13.0

- 2695 SGMR 4 S/F 1615.1 1616.1 3.0 28.0 CL-6 ST=2 TYP=3 2800 OTTA 29 PBI 1619.0 1619.0 20.0 5.2 2.6

Reports are received routinely from the following observatories: ATHN = Athens HUAN = Huancayo NAGO = Nagoya °0TS = Potsdam

BERN = Berne IRKU = 1 rkutsk N06E = Nobeyama SA0P = Sao Paj 1

o

BORD = Bordeau IZMI = IZMIRAN ONDR = Ondrej ov SGMR = Sagamore Hill CR IM = Cr imea KISV = Ki slovodsk OTTA = Ottawa TORN = Torun

DW 1 N = Dw i nge 1DO KRAK = Krakow PALE = Pa 1 ehua TYKW = Toyokawa

GORK = Gorky LEAR = Learmonth PEKG = Pek i ng TRST = Trieste

H IRA = H I rai so MANI = Man i 1 a PENT = Penticton UP 1C = Up ice V0R0 = Vorosh i 1 ov Explanation of Type Code:

1 Simple 1 7 M i nor + 24 R i se 30 Post Burst Increase A 43 Onset of Noi se Storm

2 Simple IF 8 Spike 25 Rise A 31 Post Burst Decrease 44 Noise Storm in Progress

3 Simple 2 20 Simple 3 26 F a 1 1 33 Absorption 45 Complex

4 Simple 2F 21 Simple 3A 27 R 1 se and Fall 40 F 1 uctuat ion 46 Comp 1 ex_ F

5 Simple 22 Simple 3F 28 Precursor 41 Group of Bursts <1 Great Bur^t

6 M i nor 23 Simple 3AF 29 Post Burst Increase 42 Series of Bursts 48 Major

1 A Simple 1

4A Simple 2AF 24PF Post R i se F 27F Rise and Fal 1 F 3A Simple 2A 240 Rise on 1 y 16A Fat 1 A 27AF Ri se and F a 1 1 AF 21A Simple 3A GRF 240F Rise only F 260 Fall Only 31A Post Burst Decrease A 2A Simple 1AF 24P Post Rise 26F Fall F 32A Absorption A 46F Complex F Remarks

QL = Quality (

1 =poor to 6=excel lent) ST = Status (1=real time; 2= final ; 3=correct ion ; 4=deletion) TYP= Type (1=noise storm;2=r!se In base level ; 3=minor;4=group;5=major;6=major plus;7=Castel I i U-type burst)

Figure 4.

avoi ded

Selected, short duration,

during the G/T measurement

radio emissions,

days are contained

Maj or

in the

events to be

boxes

.

14
Figure 5. Hypothetical flux density curves.

Figure 6. Smoothed solar flux density at 8.8 GHz measured by AFGl f ' January to August 1979.

15
35.3 GHz

0.2

9.4 GHz

3.3 GHz

1.4 GHz

o.i

0.0

€ = 0

0.2

0.1

0.0

J

\

I

€ = 0.3

Figure 7. Quiet -sun brightness temperature profiles (in units of 10^ kelvins)

at various frequencies. The solid curves are equatorial profiles, and the

dashed curves are polar profiles. The values of e represent the

ellipticity at the half-power levels indicated. The abscissa is in units

of the optical solar radius. (After Kundu [9].)

16
17

Figure

8.

Effective

solar

rf

diameter

(d)

in

units

of

the

optical

diameter

(dQ)

versus

frequency

for

two

ratios

(1%

and

10%)

of

contour

temperature

to

apparent

temperature.

(After

Smerd

[16].)
p Table 1. Average flux density S(W/m /Hz) versus frequency for the quiet sun radiation in terms of the base-10 logarithm of S. (From Allen [10].)

QUIET SUN RADIATION

FREQUENCY (GHz) Log S

10 2.48

20 2.93

50 3.57

100 4.125

200 4.69

500 5.47

18
NBS-I 14A REV. 2-g U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR 84-3015

2. Performing Organ. Report No, 3. Publication Date August 1984

4 . TITLE AND SUBTITLE

A Preliminary Investigation Into Using the Sun as a Source for G/T Measurements

5. AUTHOR(S)

William C. Daywitt

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

NATIONAL bureau of standards

department of commerce

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

Same as 6

10. SUPPLEMENTARY NOTES

1 Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bi bl iography or literature survey, mention it here) This report describes a preliminary investigation into determining the solar

flux density, the atmospheric correction factor, and the star shape correction factor

for use in G/T measurements above 5 GHz. An estimate of errors is also included. Preliminary results show: an improved algorithm for determining diffusive and refractive

attenuation; a viable technique for estimating the solar flux density from daily

AFGL flux density measurements and a centimeter/millimeter wave spectrum function; an the possibility of reducing star shape correction factor errors by use of»an effective

solar rf diameter.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon sj atmospheric correction factor; earth terminal measurement system; error analysis;

G/T; solar flux density; star shape correction factor

13. AVAILABILITY

| xl Uni imited

| | For Official Distribution. Do Not Release to NTIS

[2ZI Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

|_Xj Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

24

15. Price

$7.00
n

h